Concept:
Water absorption is an important property used to judge the quality of bricks. Excessive water absorption indicates high porosity, which reduces the strength and durability of the brick.
According to IS specifications, a first-class brick should not absorb more than \(20\%\) of its dry weight after being immersed in water for 24 hours.
Step 1: State the water absorption test.
Let
\[
W_d=\text{Dry weight of the brick},
\]
and
\[
W_w=\text{Weight after immersion in water for 24 hours}.
\]
The percentage water absorption is
\[
\%\text{Water Absorption}
=
\frac{W_w-W_d}{W_d}\times100.
\]
Step 2: Apply the standard requirement.
For a good quality brick,
\[
\%\text{Water Absorption}\le20\%.
\]
Hence, a good brick should not absorb more than
\[
\boxed{20\%\text{ of its dry weight}.}
\]
Therefore, the correct option is
\[
\boxed{(A)\;20\%\text{ of its dry weight}.}
\]